Even in 1811, the gridiron did not work well. For the small single-family row house which predominated at that time, the solar orientation of the gridiron was reversed from the ideal. Had the long dimension of each block faced east-west, both front and rear facades of each house would have received sunlight each day; however, with the north-south orientation, the south facades received all of the sun, and the north facades received none. In addition, no service alleys were provided through the centers of the blocks, although this was the usual practice in gridiron planning. As a result, the Manhattan grid was substandard. Yet it remained inviolate for more than a century, except for Central Park, which was set aside in 1853. Unfortunately, these flaws were repeated as Brooklyn, Queens, and the Bronx were developed. For housing design, it was not until well into the twentieth century that the gridiron was tampered with – in the large government-subsidized projects of the New Deal. [...]

By the 1870s a consensus among architects had developed that the Manhattan gridiron was a deterrent to the city's architectural advancement. Objections were aesthetic, as well as functional. They believed the possibilities for a great architecture in New York City were hampered by the gridiron. The landscape architect [and co-designer of Central Park] Frederick Law Olmsted wrote in 1876 that:

"[...] There are numerous structures, both public and private, in London and Paris, and most other large towns of Europe, which could not be built in New York, for want of a site of suitable extent and proportions. The trustees of Columbia College sought for years to obtain the privilege of consolidating two of the uniform blocks of the system, into which their own property had been divided, in order to erect sufficient buildings for their purposes, in one unbroken group, but it was denied them."

Olmsted also noted that the lack fo service alleys hindered building at higher densities by eliminating the possibility of developing legitimate streets at the interior of the blocks whenever necessary. He argued that without alleys, only 100-ft lots were possible, when shorter ones could be more useful for certain applications:

"In New York, lots of 100 feet in depth cannot be afforded for small, cheap houses. The ground-rent would be in too large proportion to the rent of the betterments. In no prosperous old city are families of moderate means found living, except temporarily in the outskirts, in separate houses on undivided blocks measuring 200 feet from thoroughfare to thoroughfare. It is hardly to be hoped that they ever will be in New York under the plan of [1811]."

The excessive depth of the lots and lack of interior alleys inherent in the Commissioners' Plan had significant health and hygiene ramifications for the so-called "tenements," which would prove problematic throughout the nineteenth century century. Various building regulations, de facto and de jure, tried to compensate for the defects of the Manhattan grid, but it wasn't until the end of the century that advances in healthcare, building, and transit overcame the practical limitations of the ubiquitous 200-ft deep block.

And if you're interested in an alternate history of Manhattan streets, Old Urbanist's got you covered.